Emergence may be defined as the appearance of qualitatively unique collective properties in a macroscopic system that are unpredictable from knowledge of its microscopic elements. Thus, the key to understanding emergence lies not in the details of the microscopic elements themselves, but rather in the interactions between them. A vast literature is built on linear analyses of synchrony in neuronal ensembles, but recent work has revealed that nonlinear synchronous activities are also present. The PI is a theoretical physicist with a background in nonlinear dynamics that has been developing a thermodynamic formalism that quantitatively describes transitions between synchronous states in systems of coupled nonlinear elements. This Mentored Quantitative Research Career Development Award will permit the PI to acquire training in neuroscience and neuroscience laboratory techniques, and to use these skills to extend and productively apply these new theoretical tools to biomedical applications. Accordingly, the long-term career goal of the PI is to become an effective researcher in the biomedical applications of dynamical systems theory, with specific emphasis on neuroscience. The theme of this research plan is: Emergent phenomena in neuronal ensemble dynamics are related to small-scale interactions between large numbers of individual neurons or groups of neurons. These interactions involve both linear and nonlinear states of synchronous activity, have structure in both time and space, and are describable within a thermodynamic formalism. Specific hypotheses to be investigated are: (1) macroscopic phenomena in neuronal ensembles (e.g., bursting and seizing events) are explained by synchronous activity between individual neurons; (2) emergent phenomena require large numbers of interacting neurons; and (3) spatially propagating waves of synchronous activity occur in neuronal ensembles. Several specific experiments monitoring individual neuronal behavior and simultaneous population activity during bursting and seizing are proposed to probe the hierarchy and structure of synchronization states.